How to map an Image on a plane manually?
Open your image in the UV/Image editor, Press N to open the side panel. In the image section you can see the image's dimensions in pixels.



Add a plane and scale it so that it has the same proportions of your image.

Int this example the image is 1728 x 2592 pixels, so I scaled the plane to

1.728 x 2.592

At this point press Ctrl+A to apply the scale. (for more on this read: Why is it important to apply transformation to an objects data?)

Then go to top view. Enter edit mode, press U to unwrap the UVs and select "Project From View (bounds)".



That will create a UV map that matches with the image used.



Then, just create a material that uses an image texture, and select the image you are using as a source, using UV as the mapping coordinates.

For Cycles:



For Blender Internal:


After doing all of this, you might want to save all of the trouble and just use the "add images as planes" addon, that does all of this for you atomatically, but at least you know what happens behind the scenes...